<TITLE>prob019: magic squares and sequences</TITLE>
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<H1>prob019: magic squares and sequences</H1>

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<TR> <TD> proposed by
     <TD ALIGN=LEFT> <A HREF="http://dream.dai.ed.ac.uk/group/tw">
          <B>Toby Walsh</B></A> 
          <ADDRESS><a href="mailto:tw@cs.strath.ac.uk">
          tw@cs.strath.ac.uk</a></ADDRESS>
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<H3> Results </H3>

The smallest magic square is, of course, 1 by 1.
There is no 2 by 2 magic square. There are, however,
3 by 3 magic squares. According to the Guiness Book
of Records, the
<A HREF="http://www.recordholders.org/en/records/magic.html">largest known magic square</A>
is 3001 by 3001 and was computed by Louis Caya (Sainte-Foy, Canada) in 1994.

<P>
Many examples of magic squares can be found
<A HREF="http://www.pse.che.tohoku.ac.jp/~msuzuki/MagicSquare.html">online</A>.

<P>
The smallest anti-magic square is 3 by 3.
<A HREF="http://www.uwinnipeg.ca/~jcormie/construct.html">Constructions</A>
exist for building anti-magic squares of larger sizes, but
these do not give all possible squares. 

<P>
Eliminating symmetry would appear to be very important in these
problems, especially
when counting solutions or proving none exits. 

<P>



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